\documentclass{article}
\begin{document}
\[
\frac{\frac{{\forall (p2,\exists (p3,r))}\quad\frac{\frac{{\forall (p1,\exists (p2,r))}\quad\frac{{\exists (p1,\forall (pn,\neg r))}}{\exists (p1,p1)}{I}}{\exists (p1,\exists (p2,r))}{D1}}{\exists (p2,p2)}{II}}{\exists (p2,\exists (p3,r))}{D1}}{\exists (p3,p3)}{II}
\]
\end{document}
